1. Field of the Invention
This invention relates generally to control systems for use in an automated manufacturing process. More specifically, the invention relates to closed-loop feedback control for maximizing a process capability index in a progressive forming operation, especially for high-precision, high-volume applications.
2. Background
Process capability index, or Cpk, is a well-known statistical measurement used to indicate how well a process or products of the process conform to specifications. Mathematically, Cpk may be defined as the lesser result of two calculations: (1) Cpk=(USL−mean)/(3×sigma) and (2) Cpk=(mean−LSL)/(3×sigma); where USL and LSL are the upper and lower specification limits, respectively, and sigma is the standard deviation of some probability distribution within those limits. Generally speaking, given a target value within the specification limits, Cpk measures two qualities: product variation relative to a mean, and how closely the mean converges on the target. Cpk is often used as an indicator of product quality in statistical process control, sometimes as an alternative to sigma. Assuming a normal distribution of data resulting from a stable process, and a standard sigma shift of 1.5, a Cpk value of 2.00 is equivalent to the standard value of 6.00 sigma. Under these conditions, a rule of thumb in statistical process control is to maintain Cpk at or above 1.33 (i.e. 4.00 sigma), in order to ensure product conformance.
Statistical process controls employing Cpk can been applied, for example, to processes that use progressive tooling die for automated mass production of high-precision components. Typically, the progressive die consists of multiple forming stations, where each station is configured to perform one or many forming operations on incoming product. The forming operations may perform stamping, coining, cutting, punching, bending, welding, drilling, plating, or other tooling functions. A quantity of incoming or unformed product is fed serially into the process, and the various forming operations are carried out in sequence as the product advances from station to station. Some imperfections affecting Cpk may be present in the unformed product prior to processing, while others may be introduced by action of the forming stations. Variations introduced at a forming station may result from erratic component alignment or other imperfect tooling construction or operation. For small, high-precision components, environmental factors such as variations in temperature, humidity, and pressure may also contribute to lower Cpk. Other defects that adversely affect Cpk may be traced to random errors caused by control system transients or defects in raw material.
Conventional methods for forming precision features on small parts rely on highly precise tooling and guiding means to register incoming material to the form tooling. This is typically achieved by configuring unformed or partially formed components onto a fret at regular intervals. The fret is also configured with precision locating features, such as holes, that match precision tooling features, such as positioning pins, that are located on a feed mechanism or feed bar. Using these features, the feed mechanism holds and positions the fret as it incrementally advances past each forming station in the progressive die set. The accuracy of the final formed component is thus a function of the cumulative errors in the fret, in the positioning mechanism, and in the registration of each die position. Cumulative errors are particularly troublesome in high-precision forming operations, where tolerances are on the order of 100 microns or less.
When the number of forming stations required to produce the correct part geometry number more than one, establishing these stations in a correct relationship can be a costly and time-consuming calibration. This process of maintaining hard tooling typically requires manual internal setup of the forming stations. Inevitably, hard tooling leads to a loss of capacity whenever a station in the progressive die drifts out of tolerance, interrupting production until it can be re-calibrated, often by manual trial and error.
To have sufficient capacity to meet demand and to compensate for a production line being out of service, a manufacturer may establish multiple production lines for parallel manufacturing of a common component. However, this approach tends to decrease Cpk for the overall population of manufactured goods when goods from different production lines are commingled. FIG. 1 illustrates this phenomenon. Parallel production lines L1(1), L1(2), . . . and L1(n) are each hard-tooled to produce, through respective forming processes 102, 104, 106, a relatively narrow distribution between LSL and USL, as indicated by the respective curves 108, 110, 112. Each of these distributions exhibits a Cpk value between 1.33 and 2.00. Note, however, the disparity among curves as to how closely each mean converges on its target T. In the aggregate, these curves combine to form curve 114, which represents a distribution of output from multiple production lines commingled into a single lot, for example, to satisfy a purchase order. Thus, the combined distribution curve 114, seen by the customer, exhibits a much wider distribution that may correspond to a Cpk below the customer's acceptance criteria.
As market forces continue to demand tighter tolerances for precision components, there is an ongoing need to sharpen process controls to maintain Cpk at acceptable levels.